Contributed Seminar: Stochastic thermodynamics: Energy Conservation and entropy production along a single trajectory

Abstract

For stochastic dynamics of driven non-equilibrium systems, entropy production can be defined along a single trajectory [1]. It consists of two parts, entropy change of the system itself and entropy change of the surrounding medium. Total entropy production fulfills an integral fluctuation theorem for arbitrary initial state and arbitrary driving. For steady states, the total entropy production obeys the detailed fluctuation theorem even for finite times. These theorems can be derived without the notion of a surrounding heat bath of constant temperature. In the presence of such a bath as it is typical for many colloidal and biomolecular systems, however, a first law-like energy balance along the trajectory allows to identify dissipated heat and equate it with the entropy change of the medium.

I will sketch the derivation of these results both for a Langevin type dynamics of continuous degrees of freedom and for a master equation dynamics on a discrete set of states. Illustrative examples for the first type include our recent experiments on a colloidal particle in a time-dependent non-harmonic potential [2]. Examples for discrete dynamics include enzym models [3,4] and our experiments on an athermal optically driven two-level system [5].